OK, now I have processed 35k pieces of brass with the Lyman dies and probably loaded 12k. I've also compared them with the Redding, including some of the new nxGen Redding dies. Here is, die by die, what I am seeing:
1- Sizing die: Both the Lyman Pro and Redding nxgen sizing dies have extended length carbide sleeves, which are much longer than the old carbide rings that Dillon told people gave great ammo while looking like wasp waisted crap. The new carbide sleeves give all of the nck tension of a Dillon die, without oversizing the middle, which is especially bad in a 9mm, which is tapered. The Lyman and Redding dies give identical measurements at the casehead and at the mouth, but I rollsize, so casehead measurements could be impacted by this. However, when I process brass I run it at 3500 rounds per hour nominal (2850 actual) and the slight rounding of the sleeve at the base of the Lyman dies means that I never get a casemouth impact, while the very square Redding base gives occasional impact, and thus damaged brass. The Lyman sleeve is also thicker, but this makes no difference as far as I know. So, if you are running manually, they are equal. If you are pushing the speed, the Lyman is better. The Lyman decapping rod is slightly better, though I decap before sizing.
2- Lyman has a hold down die, and Redding doesn't. I don't use Lyman's hold down die, although it seems fine.
3- The Redding expander is titanium nitride coated, and the Lyman is black. I don't know what coating it has, but it is just about as slick as the Redding. Maybe nitride? The Lyman has no upper adjustment, just screw it into the press. The Redding has the coarse screw into press adjustment and fine top adjustment. I get just about the same results either way.
4- The seaters are similar in that they are both micrometer and sprung, but work differently. The Redding is pretty standard in that it catches the bullet up in the die, and stabilizes it at the end of the seating process. The Lyman seating stem protrudes below the die body, and goes all the way up under spring tension. In this way, the Lyman is probably a bit better. On the other hand, the Redding stem shapes are a good bit better, especially in 45 where it catches SWC bullets right on the shoulder, which is great because a lot of SWC powder coat noses have some blobbiness leading to inconsistent depths. The 9mm stems are very similar, though. The Lyman 45 hp/swc stem is really bad, just a flat cylinder. I bedded mine with JB Weld, and now it seats great, but it isn't exactly versatile. So I'd say the Lyman may be slightly better in 9mm, the Redding is much better in 45.
5- The crimp dies are both micrometer. Well, Redding has a standard one, but mine is a micrometer. It is nice not to have to loosen the lock ring to adjust crimp, but it really isn't as big an advantage as it sounds. I guess the Redding sleeve has the slight advantage of being reversible 9/38 and 45acp/45GAP, but that doesn't help me. For both of them, however, you really end up running them pretty close to all the way down with the body and microadjust.
All in all, I'd say equal, depending on what you are looking to do.